If f(x) = (x^1/x^m)^(1+m) (x^m/x^n)^(m+n) (x^n/x^1)^(n + 1), then f'(x) is equal to A. 1 B. 0 C. x^(ℓ+m +n) D. none of these

Question

If f(x) = \(\Big(\cfrac{\text x^1}{\text x^m}\Big)^{1+m}\)\(\Big(\cfrac{\text x^m}{\text x^n}\Big)^{m+n}\)\(\Big(\cfrac{\text x^n}{\text x^1}\Big)^{n+1}\),  then f'(x) is equal to

A. 1

B. 0

C. x^{(ℓ+m +n)}

D. none of these

Answer 1

Correct option is B. 0

Differentiating w.r.t x 

⇒ \(\cfrac{dy}{d\text x}\) = 0